A property of charged particle therapy, such as proton therapy, includes the sharp fall-off of the dose-to-depth distribution induced by a charged particle beam traversing a body. This distribution is, however, sensitive to variations of the water equivalent depth (“WED”) in tissues along a beam direction of the charged particle beam. This leads to uncertainties in treatment planning. Thus, a direct verification of the WED of a charged particle beam in a body is desirable.
In Lu, Hsiao-Ming, A Potential Method for In Vivo Range Verification in Proton Therapy Treatment, Phys. Med. Biol. 53, pp. 1413-1424 (2008) (the “Lu publication”), the time dependent response of a charged particle beam detector, such as an ionization chamber exposed to a time-dependent energy modulated proton beam, was studied as a function of the depth of the charged particle beam detector in a water tank.
To produce a time-dependent energy modulated proton beam, a modulator wheel as disclosed in the Lu publication may be employed. Such a wheel typically contains different segments of absorbing materials with various thicknesses. As the modulator wheel rotates, typically at a constant speed of 600 rotations per minute, the charged particle beam passes through one segment at a time. As a consequence, a charged particle beam that is time modulated between a minimum and maximum energy value is induced at the exit of the modulator wheel.
From the results of the survey published in the Lu publication, it was shown that a charged particle beam detector exposed to a charged particle beam that is time modulated in energy presents time dependent patterns that are characteristic of the depth at which the charged particle beam detector is placed in a water tank. So, these patterns may be employed as a unique coding of the WEDs. The collection of the patterns at different depths of the charged particle beam detector may be viewed as forming a ruler, where each mark corresponds to a unique pattern. This ruler may be obtained during a calibration phase by measurement or by calculation of the time dependent response of a charged particle beam detector that is placed (or assumed to be placed) at different depths in a phantom, such as a water tank. Afterwards, by positioning the charged particle beam detector used in the calibration phase at a reference point (e.g., a target in a body), the WED corresponding to this reference point may be deduced by matching the pattern measured by the charged particle beam detector at the reference point to one of the patterns determined in the calibration phase.
The Lu publication proposes a method for this pattern matching that is minimizing the following least-square differenceL(x)=∫0T[λƒm(t)−ƒr(x,t)]2dt  (Eq. 1)with respect to depth x. The depth x corresponding to the minimum value of L(x) is the sought WED. The function ƒr(x,t) represents the patterns determined during the calibration phase, and ƒm(t) is the measured time dependent response of the charged particle beam detector positioned at the WED to be determined. The function L(x) is also minimized with respect to a scale factor λ because the pattern matching has to be purely based on the shape of the time dependence of the measured signal, independently of its absolute magnitude.
By using the method proposed in the Lu publication, one can hope to have a WED precision of about 1 mm in a homogeneous water phantom. A drawback of the method proposed by the Lu publication is the necessity to measure enough patterns at enough different depths during the calibration phase when a fine WED resolution is wanted. This leads to a relatively long calibration phase when such a fine WED resolution is desired.